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EXPERIMENTAL RESULTS OF INTEGRAL SLIDING MODE
CONTROLLER FOR A NONHOLONOMIC MOBILE ROBOT
Alaa Dib and Houria Siguerdidjane
SUPELEC, Systems Sciences (E3S), 91192, Gif-sur-Yvette cedex, France
Keywords:
Mobile Robot, Trajectory Tracking, Integral Sliding Mode, Nonholonomic systems.
Abstract:
This paper addresses the trajectory tracking problem of a nonholonomic mobile robot. More precisely, we are
interested in solving the problem of tracking a reference trajectory in presence of disturbances. A control strat-
egy based on the Integral Sliding Mode is proposed combined with a state feedback linearization. While many
studies have considered the kinematic model of the vehicle only, we have used both kinematic and dynamic
models. The distinctive property of the proposed controller is its robustness of performance in the presence
of uncertainties. To assess the quality of the proposed approach, we performed in addition to simulations the
implementation of this controller on the robot Koala, a two-wheel differentially driven mobile robot. Lab work
illustrates the real quality and efficiency of this control strategy.
1 INTRODUCTION
The motion control of mechanical systems under non-
holonomic constraints has received much attention
during past years. Wheeled mobile robots and car-
like vehicles are typical examples of such systems. As
pointed out in an early paper of Brockett (Brockett,
1983), such control systems cannot be stabilized by
continuously differentiable, time invariant, state feed-
back control laws. Another difficulty in controlling
nonholonomic mobile robots is that in the real world
there are uncertainties in their modeling. Taking into
account intrinsic characteristics of mobile robots such
as actual vehicle dynamics, inertia and power limits of
actuators and localization errors, their dynamic equa-
tions could not be described as a simplified mathemat-
ical model. This has attracted interest of researchers
to the problem of nonholonomic mobile robot con-
trol. Discontinuous state feedback controller is used
(Astolfi, 1995), (Astolfi, 1996)), tracking control us-
ing direct Lyapunov method (D’Andrea-Novel et al.,
1995), time variant state feedback (Samson, 1995),
(Walsh et al., 1994). Stabilization and control of non-
holonomic systems with dynamic equations are pre-
sented in (Bloch et al., 1992), backstepping based
methods has been considered in several papers (Fierro
and Lewis, 1997), (Jiang and Nijmeijer, 1997), (Tan-
ner and Kyriakopoulos, 2002) and a switched finite-
time control algorithm has been proposed in (Banavar
and Sankaranarayanan, 2006).
Sliding mode control has been applied to the tra-
jectory control of robot manipulators (Slotine and
Sastry, 1983), (Yeung and Chen, 1988), and is receiv-
ing increasing attention from researches on control
of nonholonomic systems with uncertainties. For ex-
ample, in (Guldner and Utkin, 1994) a sliding mode
control was used to guarantee exact tracking of tra-
jectories made by navigation functions. In (Yang and
Kim, 1999) a sliding mode control law is proposed for
asymptotically stabilizing the mobile robot to a de-
sired trajectory, where robot posture was represented
using polar coordinates. The benefits of the sliding
mode command which makes it very important is its
robustness with regards to disturbances and structural
uncertainties, i. e. the system response depends on the
gradient of the sliding surface and remains insensitive
to variations of system parameters and external distur-
bances. However, during the reaching phase (before
Sliding Mode occurs), the system has no such insen-
sitivity property; therefore, insensitivity cannot be en-
sured throughout an entire response. The robustness
during the reaching phase is normally improved by
high-gain feedback control. Stability problems that
arise inevitably limit the application of such high-gain
feedback control schemes.
In this paper, we propose to perform a feedback
linearization for a class of nonholonomic dynamic
systems, combined with an Integral Sliding Mode
controller which concentrates on the robustness of the
motion in the whole state space. The order of the mo-
tion equation in this type of Sliding Mode is equal
to the dimension of the state space. Therefore, the
robustness of the system can be guaranteed through-
out an entire response of the system starting from the
445
Dib A. and Siguerdidjane H..
EXPERIMENTAL RESULTS OF INTEGRAL SLIDING MODE CONTROLLER FOR A NONHOLONOMIC MOBILE ROBOT.
DOI: 10.5220/0003648904450450
In Proceedings of the 8th International Conference on Informatics in Control, Automation and Robotics (MORAS-2011), pages 445-450
ISBN: 978-989-8425-75-1
Copyright
c
2011 SCITEPRESS (Science and Technology Publications, Lda.)